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A NOTE ON THE FIRST LAYERS OF ℤp-EXTENSIONS
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 Title & Authors
A NOTE ON THE FIRST LAYERS OF ℤp-EXTENSIONS
Oh, Jang-Heon;
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 Abstract
In this paper we explicitly compute a Minkowski unit of a real abelian field and give a criterion when the first layer of anti-cyclotomic -extension of an imaginary quadratic field is unramified everywhere.
 Keywords
Minkowski unit;anti-cyclotomic extension;-extension;
 Language
English
 Cited by
1.
A p-TH ROOT OF A MINKOWSKI UNIT,;

충청수학회지, 2010. vol.23. 4, pp.625-628
2.
CONSTRUCTION OF THE FIRST LAYER OF ANTI-CYCLOTOMIC EXTENSION,;

Korean Journal of Mathematics, 2013. vol.21. 3, pp.265-270 crossref(new window)
3.
ON THE ANTICYCLOTOMIC ℤp-EXTENSION OF AN IMAGINARY QUADRATIC FIELD,;

Korean Journal of Mathematics, 2015. vol.23. 3, pp.323-326 crossref(new window)
1.
ANTI-CYCLOTOMIC EXTENSION AND HILBERT CLASS FIELD, Journal of the Chungcheong Mathematical Society, 2012, 25, 1, 91  crossref(new windwow)
2.
ON THE ANTICYCLOTOMIC ℤp-EXTENSION OF AN IMAGINARY QUADRATIC FIELD, Korean Journal of Mathematics, 2015, 23, 3, 323  crossref(new windwow)
3.
CONSTRUCTION OF THE FIRST LAYER OF ANTI-CYCLOTOMIC EXTENSION, Korean Journal of Mathematics, 2013, 21, 3, 265  crossref(new windwow)
 References
1.
J. Minardi, Iwasawa modules for $Z_p^d$-extensions of algebraic number fields, Ph. D. dissertation, University of Washington, 1986.

2.
J. Oh, Defining Polynomial of the first layer of anti-cyclotomic $\mathbb{Z}_3$-extension of imaginary quadratic fields of class number 1, Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), no. 3, 18-19. crossref(new window)

3.
J. Oh, The first layer of $\mathbb{Z}^2_2$-extension over imaginary quadratic fields, Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), no. 9, 132-134. crossref(new window)

4.
J. Oh, , On the first layer of anti-cyclotomic $\mathbb{Z}_p$-extension of imaginary quadratic fields, Proc. Japan Acad. Ser. A Math. Sci. 83 (2007), no. 3, 19-20. crossref(new window)

5.
L. Washington, Introduction to Cyclotomic Fields, Graduate Text in Math. Vol. 83, Springer-Verlag, 1982.